**Interest**, in finance and economics, is payment from a borrower or deposit-taking financial institution to a lender or depositor of an amount above repayment of the principal sum (that is, the amount borrowed), at a particular rate. It is distinct from a fee which the borrower may pay the lender or some third party. It is also distinct from dividend which is paid by a company to its shareholders (owners) from its profit or reserve, but not at a particular rate decided beforehand, rather on a pro rata basis as a share in the reward gained by risk taking entrepreneurs when the revenue earned exceeds the total costs.

For example, a customer would usually pay interest to borrow from a bank, so they pay the bank an amount which is more than the amount they borrowed; or a customer may earn interest on their savings, and so they may withdraw more than they originally deposited. In the case of savings, the customer is the lender, and the bank plays the role of the borrower.

Interest differs from profit, in that interest is received by a lender, whereas profit is received by the owner of an asset, investment or enterprise. (Interest may be part or the whole of the profit on an investment, but the two concepts are distinct from each other from an accounting perspective.)

The rate of interest is equal to the interest amount paid or received over a particular period divided by the principal sum borrowed or lent (usually expressed as a percentage).

Compound interest means that interest is earned on prior interest in addition to the principal. Due to compounding, the total amount of debt grows exponentially, and its mathematical study led to the discovery of the number e. In practice, interest is most often calculated on a daily, monthly, or yearly basis, and its impact is influenced greatly by its compounding rate.

Our Interest Calculator can help determine the interest payments and final balances on not only fixed principal amounts, but also additional periodic contributions. There are also optional factors available for consideration such as tax on interest income and inflation. To understand and compare the different ways in which interest can be compounded, please visit our Compound Interest Calculator instead.

Interest is the compensation paid by the borrower to the lender for the use of money as a percent, or an amount. The concept of interest is the backbone behind most financial instruments in the world. While interest is earned, it is different from profit in that it is received by a lender as opposed to the owner of an asset or investment, though interest can be part of profit on an investment.

There are two distinct methods of accumulating interest, categorized into simple interest or compound interest.

The following is a basic example of how interest works. Derek would like to borrow $100 (usually called the principal) from the bank for one year. The bank wants 10% interest on it. To calculate interest:

$100 × 10% = $10

This interest is added to the principal, and the sum becomes Derek's required repayment to the bank.

$100 + $10 = $110

Derek owes the bank $110 a year later, $100 for the principal and $10 as interest.

Let's assume that Derek wanted to borrow $100 for two years instead of one, and the bank calculates interest annually. He would simply be charged the interest rate twice, once at the end of each year.

$100 + $10(year 1) + $10(year 2) = $120

Derek owes the bank $120 two years later, $100 for the principal and $20 as interest.

The formula to calculate simple interest is:

interest = (principal) × (interest rate) × (term)

When more complicated frequencies of applying interest are involved, such as monthly or daily, use formula:

interest = (principal) × (interest rate) × (term) / (frequency)

However, simple interest is very seldom used in the real world. Even when people use the everyday word 'interest', they are usually referring to interest that compounds.

Compounding interest requires more than one period, so let's go back to the example of Derek borrowing $100 from the bank for two years at a 10% interest rate. For the first year, we calculate interest as usual.

$100 × 10% = $10

This interest is added to the principal, and the sum becomes Derek's required repayment to the bank for that present time.

$100 + $10 = $110

However, the year ends, and in comes another period. For compounding interest, rather than the original amount, the principal + any interest accumulated since, is used. In Derek's case:

$110 × 10% = $11

Derek's interest charge at the end of year 2 is $11. This is added to what is owed after year 1:

$110 + $11 = $121

When the loan ends, the bank collects $121 from Derek instead of $120 if it were calculated using simple interest instead. This is because interest is also earned on interest.

The more frequently interest is compounded within a time period, the higher the interest will be earned on an original principal. The following is a graph from Wikipedia showing just that, a $1,000 investment at various compounding frequencies earning 20% interest.

There is little difference during the beginning between all frequencies, but over time they slowly start to diverge. This is the power of compound interest everyone likes to talk about, illustrated in a concise graph. Continuous compound will always have the highest return, due to its use of the mathematical limit of the frequency of compounding that can occur within a specified time period.

Anyone who wants to estimate compound interest in their head may find the rule of 72 very useful. Not for exact calculations as given by financial calculators, but to get ideas for ballpark figures. It states that in order to find the number of years (n) required to double a certain amount of money with any interest rate, simply divide 72 by that same rate.

n = 72/8 = 9

It will take 9 years for the $1,000 to become $2,000 at 8% interest. This formula works best for interest rates between 6 and 10%, but it should also work reasonably well for anything below 20%.

The interest rate of a loan or savings can be "fixed" or "floating". Floating rate loans or savings are normally based on some reference rate, such as the U.S. Federal Reserve (Fed) funds rate or the LIBOR (London Interbank Offered Rate). Normally, the loan rate is a little higher and the savings rate is a little lower than the reference rate. The difference goes to the profit of the bank. Both the Fed rate and LIBOR are short-term inter-bank interest rates, but the Fed rate is the main tool that the Federal Reserve uses to influence the supply of money in the U.S. economy. LIBOR is a commercial rate calculated from prevailing interest rates between highly credit-worthy institutions. Our Interest Calculator deals with fixed interest rates only.

An important distinction to make regarding contributions are whether they occur at the beginning or end of compounding periods. Periodic payments that occur at the end have one less interest period total per contribution.

Some forms of interest income are subject to taxes, including bonds, savings, and certificate of deposits(CDs). In the United States, corporate bonds are almost always taxed. Certain types are fully taxed while others are partially taxed; for example, while interest earned on U.S. federal treasury bonds may be taxed at the federal level, they are exempt at the state and local level. Taxes can have very big impacts on the end balance. For example, if Derek saves $100 at 6% for 20 years, he will get:

$100 × (1 + 6%)20 = $320.71

This is tax-free. However, if Derek has a marginal tax rate of 25%, he will end up with $239.78 only because the tax rate of 25% applies to each compounding period.

Inflation is defined as an increase in the general level of prices, where a fixed amount of money will relatively afford less. The average inflation rate in the United States in the past 100 years has hovered around 3%. As a tool of comparison, the average annual return rate of the S&P 500 (Standard & Poor's) index in the United States is around 10%. Please refer to our Inflation Calculator for more detailed information about inflation.

Leave the inflation rate at 0 for quick, generalized results. But for real and accurate numbers, it is possible to input figures in order to account for inflation.

Tax and inflation combined makes it hard to grow the real value of money. For example, in the United States, the middle class has a marginal tax rate of 25% and the average inflation rate is 3%. To maintain the value of the money, a stable interest rate or investment return rate of 4% or above needs to be earned, and this is not easy to achieve.

assume your deposit hundred rupees in abank at a rate of 10% what does thisexactly mean we know that 10% of 100 is10 so if you deposit 100 rupees with abank you will get 100 10 rupees at theend of the year but what about thesecond year the third year and so onlet's make three columns the year theinterest and the total interest at theend of the year let's also make a columnfor the amount for each year so we havefour columns now and remember the amountis the sum of the principal and theinterest the principal in this case willbe the deposit amount which is 100rupees let's see what happens in year 1because you get an interest of 10% fromthe bank you will get 10 rupees asinterest what happens if you keep themoney with the bank for another year youwill get another 10 rupees as interestand if you keep the hundred rupees forone more year you again get 10 rupees asinterest that is simple interest if youkeep your money deposited with a bankyou get the same interest every yearlook at it this way your principal willremain in the bank until you withdraw itat the end of the first year the bankpays you an interest of 10 percent onthis 100 rupees principle that's 10rupees these 10 rupees will accrue inthe bank until you decide to withdraw itagain at the end of the second year thebank pays you an interest of 10 percenton this principle 10 rupees this willaccrue until you over draw it and 10rupees accrue again at the end of thethird year every year you get aninterest on the principal you investednow let's look at the total interestcolumn if you would have taken the moneyout in the first year you would have gotan interest of 10 rupeesand the amount you would have receivedis hundred ten rupeesremember amount is the sum of theprincipal and the interest if you wouldhave taken the money out in the secondyear you would have got ten plus tenwhich is twenty rupees an amount wouldequal to hundred plus 20 which equalsone hundred twenty rupees and if youwould have taken the money out after thethird year you would have got 10 plus 10plus 10 which is thirty rupees asinterest and an amount equal to onehundred thirty rupeesone thing is clear the longer you keepyour money with the bank the more moneyyou get at the end of the period so whatare the factors that the amount isdependent on look closely it will dependon the principal or the initial depositmore the money you deposit more will bethe final amount it will also depend onthe rate of interest if instead of tenpercent the bank offered you fifteenpercent the amount you receive will behigher and of course on the number ofyears you've deposited the money if anyof these factors change the amount youwould get will also change this conceptwe just saw is called simple interestthe interest amount is based on theoriginal principal only also notice thatthe total interest after the second yearis twice the interest of ten rupees andthe interest after the third year isequal to three times the interest of tenrupees can we deduce a formula to getthe total interest after a few yearslet's consider year two we first lookedat the principal which is hundred sincethe interest is 10% we multiplied it byten by hundred and since it is thesecond young we multiplied by two thisgives us the interest in the first yearand we multiplied by two to get thetotal interest after two years if yousolve this you will get a twenty andsimilarly for year three the totalinterest will equalthree multiplied by ten by hundredmultiplied by three this will give you30 so based on this concept we willsolve an example in the next videoyou

okay so today I will introduce compoundinterest with an example with the firstquestion over here and then you can tryquestion number two on your own andafter that I will explain it as well sohere is the compound interest formulaand it will clarify each element that wehave here the B will be the initialamount invested a will be the finalamount so so far so good right R will bethe interest rate n will be the amountof times that the investment iscompounded per year so that's a prettyimportant value we have two of them inthe formula for example if in the in thefirst example here we have annualcompounding right which means that nwould be one because it's compoundedonly once a yearand finally the T of course is time youshould be writing this now maybe youalready are so here's the interest rateinterest rate time n is the number oftimes the compounds per yearwell my handwriting is horrible todayand P is the initial amount of money ais the final amount of money so forquestion number one here I have athousand dollars invested at fivepercent compounded annually so a is whatwe want to find out P is a thousand thenI have one plus R which is five percentand since we have five percent I'll needto rewrite this as 0.05 okay all I needto do is just divide the 5 by 100 so wehave point zero five divided by onethat's because it's annual compoundingfor the next one already give you a hintfor monthly compounding n is going to betwelve because then the investment iscompounded twelve times a year so thenin this case we have this ^ time in thiscase times seven seven years and time isgoing to multiply the N and n is onejust like it was one over here so let mejust make this look a little bit betterpoint zero five little bit divided by 1is just 0.2 0 5 plus 1 is one point zero5 ^ 7 because 7 times 1 is just 7 greatnow what do we do one very commonmistake is for people to multiply the1000 by the 1.05 we can't do thatbecause of PEMDAS right we have to doexponents before multiplication so we'regoing to do one point zero 5 ^ 7 firstand let me use my calculator to figurethat out so we get one point four zeroseven then we can multiply that by athousand and we get the final amount ofone thousand four hundred and sevendollars and ten cents okay so afterseven years investing at five percentcompounded annually a thousand dollarsbecomes a thousand or one hundred andseven dollars and ten cents great now Iwill suggest that you try questionnumber two on your own if you want youcan pause the video

youand now it will explain it so I'm prettystraightforward I guess I had alreadycleared up all the elements that we havehere a little different letters and soin this case we have a is equal to B theinitial amount is two thousand dollarsinvested at 12% compounded monthly so to12 percent we're going to plug it inhere for our but we're going to write itas 0.12because it's a percentage right so 12divided by 100 is 0.12 now divided by Nand is 12 because it's monthlycompounding so it compounds 12 times ayear to the power of T is 5 becausewe're investing this for 5 years andwe're multiplying the 5 by 12 becausethat's n again so we have a equals 2000times now point 12 divided by 12 is 0.01plus 1 is one point zero 1 to the powerof 60 again very popular mistake pleaseavoid it be to multiply the two thousandby the 1.01 right away we can't do thatbecause we need to do this first we needto go one point zero one to the power of60 and on we get one point eight one sixseven for that so we do this first andthen we multiply that value by twothousand two obtain three thousand sixhundred and thirty three dollars andthirty nine cents so that's it soinvesting two thousand dollars at 12%compounded monthly for five years thisis what we get so hopefully that makegreat sense to you and check up somemore videos right here good luck

Last week we talked about NUT.

and i was assuming that everybody knows how to calculate compound interest.

But after reading comments.

70% don't know how to calculate compound interest.

I guess we learned compound intererst from 7-8th class.

It's very basic

If you deposit money in bank account so the interest you get is compound interest.

SO if you don't know how to calculate this.

This is wrong. You should know.

Where you are investing , you are supposed to aware how much interest you'll get.

Let's understand this on white board

How to calculate compound interest.

Let's say i gave 1000 to someone , so what will be the value after 1 year.

at a interest of 10%

100 rs will be simple interest.

So i got 1100rs after 1 year with interest.

Next year again i'll get 100rs interest.

But logically

Next year i gave them 1100rs right?

So 100 won't be the interest according to 1100rs.

1000 + 100 = 1100rs

So in second year i should get interest at 1100rs not 1000rs.

But the bank gave 100rs interest.

Logically they should've given 110rs.

But Bank gave 100rs.

That's why simple interest formula didn't work after 1 year.

Now advanced thing i.e Compound interest.

In Compound interest you're getting 110rs in second year.

So in 1 st year you get 100rs

Next year you get 110rs.

100 + 10% of 100 = 110.

Means overall you get 110rs.

In third year , you get 100 + 10% of 110rs = calculate ;p

So if you want to calculate for 10 year then?

THis is the formula for compound interest.

P = principal amount

Like here P=1000

R is rate of interest

Rate = 10%

N = No. of year

Now what we calculated here.

Here we took the value of n = 1,2,3......

It means we are calculating compound interest manually.

You'll see somewhere that 10% compounded annually.

means 1,2,3.......

If it's compounded monthly

Then you need to calculate in terms of months.

Like you are investing somewhere for 5 years

So there are 12 months in 1 year

12*5 = 60 months

Calculate the compound interest monthly.

Your value n is 60 here.

and rate is annual rate

Let's say 12%

What we will do rate-12/12(months)

So logically rate of interest is 1% monthly.

12/12

That is 1 % of rate of interest.

Same formula of compound interest.

and then after dividing the denominator with numerator ,

and then we'll multiply that with n

That's it.

If you still didn't understand it, tell me in the comments below.

i may make an another video

I will upload a video today in the evening .It might be controversial.

I hope you'll support me.

Okat friends(dosto) , with this, video ends. I hope you liked it.

If any doubts , do ask me in the comments below.

Like share and do tell me in the comments.

Did you know how to calculate compound interest?

do tell me

If you haven't seen that NUT video.

You can check how do we calculate interest.

Here we talked about compound interest.

That we invested 1000rs in 1 year.

How much will i get after 10 years.

But if we are investing 1000 rs every year

Interest will keep on increasing.

How do we calculate that

Whether it's profitable for you or not?

We've talked about this in that video NUT

Bye Goodnight Goodmorning Goodafternoon whenever you are watching this video